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Hamiltonian dynamics on convex polytopes
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Related lectures (51)
Fundamental Solutions
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Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.
Optimal Transport: Heat Equation and Metric Spaces
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Explores optimal transport in heat equations and metric spaces.
Regular Polyhedra: Definitions and Symmetries
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Explores the definitions and symmetries of regular polyhedra, focusing on the five known convex regular polyhedra from ancient times.
Closest Vector Problem: Voronoi Cells
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Explores the Closest Vector Problem and Voronoi cells in lattice reduction algorithms.
Untitled
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Cheeger's Inequality
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Explores Cheeger's inequality and its implications in graph theory.
Sparsest Cut: Leighton-Rao Algorithm
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Covers the Leighton-Rao algorithm for finding the sparsest cut in a graph, focusing on its steps and theoretical foundations.
Convergence of Random Walks
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Explores the convergence of random walks on graphs and the properties of weighted adjacency matrices.
Fields Deriving from a Potential
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Explores fields deriving from a potential, emphasizing integral and linear aspects.
Convex Optimization: Convex Functions
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Covers the concept of convex functions and their applications in optimization problems.
Convex Optimization: Elementary Results
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Explores elementary results in convex optimization, including affine, convex, and conic hulls, proper cones, and convex functions.
Calculus of Variations: Some Topics
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Covers fundamental topics in calculus of variations, including minimizers and the Euler-Lagrange equation.
Laplace Equation: Decomposition and Solutions
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Covers the Laplace equation, decomposition of linear problems, and solutions through separation of variables.
Analysis IV: Convergence Theorems and Integrable Functions
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Covers convergence theorems and integrable functions, including the Lebesgue integral and Borel-Cantelli sets.
Diophantine Approximation: Minbowski's Theorem
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Covers Minbowski's Theorem on Diophantine Approximation and Gram-Schmidt orthogonalization.
Preliminaries in Measure Theory
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Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.
Integration on H_pxH and Arithmetic
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Explores integration on H_pxH and arithmetic properties, including norms, structures, and polynomial factorization.
Interlacing Families and Ramanujan Graphs
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Explores interlacing families, Ramanujan graphs, and their construction using signed adjacency matrices.
Proof of Strong Duality
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Covers the proof of strong duality in optimization problems and provides examples of Rayleigh quotient optimization.
Variational Problems: Quasi-Convexity
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Explores the theory of quasi-convexity in variational problems from continuum mechanics, discussing its principles, applications, and relationship with convexity.
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